The Blackmailer’s Paradox

Evelyn Gordon
Contentions/Commentary
23 August '10

With direct negotiations about to begin, Israeli negotiators should enroll in a crash course with the country’s Nobel laureate in economics, Prof. Robert Aumann. Aumann, whose specialty is game theory, offered valuable advice in an interview with Haaretz last month, in which he described a game-theory concept known as “the blackmailer’s paradox.”

“Someone offers Reuven and Shimon NIS 1,000 together, if they can manage to agree on the question of how to split the money between them. Reuven says to Shimon: ‘Great, let’s split it half and half.’ Shimon says: ‘No. I am not leaving here with less than NIS 900. You will get 100. Take it or leave it.’ Reuven says to him: ‘Be rational. What is the difference between us? Why should you get more?’ Shimon says: ‘Rational or not, do what you want. Either I leave here with 900 or with nothing. You decide.’

“Reuven thinks and says: ‘Okay, NIS 100 is money nevertheless. What am I going to do with this irrational mule? I myself am rational and I will take the 100. I need to advance my goal of getting as much money as possible, and my choice is between zero and 100. One hundred is still something.’

“What is the paradox? That the irrational person gets more than the rational person.”

The problem with Israel’s negotiations with both the Palestinians and Syria, Aumann said, is that the Arabs have successfully played the role of the blackmailer: they have convinced both themselves and Israel that their demands are sacred and must be met fully, whereas “we don’t manage to convince ourselves that anything is sacred.” And because Israel can’t convince itself, “there isn’t anything that we can convince the other side is sacred to us, that we’re willing to ‘be killed for it, rather than transgress.’”

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